## anonymous 4 years ago If a , b, and c are in Arithmetic Progression, then the straight line ax + by + c = 0 will always pass through the point: a) (- 1, -2) b) (1, -2) c) (-1 , 2) d) (1, 2)

1. anonymous

2. amistre64

we should know that the slope of the line is: -a/b

3. amistre64

0 = -a/b x - c is then what we have to conform to i believe

4. anonymous

I think so.

5. amistre64

well, -c/b on the end i spose would be more accurate

6. amistre64

when x=0, -c/b = 0 means that c=0 so: y = -a/b x seems like a fair assumption

7. amistre64

i gotta re think that :)

8. amistre64

ax +by + c = 0 ax + by = -c y = (-ax -c) /b no zero involved .....

9. asnaseer

If a, b and c are in AP, then doesn't this imply: b = a + d c = a + 2d where d is the difference between each term of the AP?

10. amistre64

good, good

11. anonymous

Then, how to proceed next?

12. amistre64

if my line equation is useful; maybe sub in so that it all speaks in a?

13. asnaseer

Then you can rewrite your equation as: ax + (a+d)y + a + 2d = 0 and see for which point this equation holds true?

14. amistre64

$y = \frac{-ax -(a+2d)}{a+d}$ would be the same set up i believe

15. asnaseer

yes it would

16. anonymous

So the exact option?

17. asnaseer

Aadarsh: just put each pair of values into the equations and see which one works

18. amistre64

a) (- 1, -2) b) (1, -2) c) (-1 , 2) d) (1, 2) trial and error .... $-2 \ =^? \frac{a -(a+2d)}{a+d}$ $-2 \ =^? \frac{-a -(a+2d)}{a+d}$ $2 \ =^? \frac{a -(a+2d)}{a+d}$ $2 \ =^? \frac{-a -(a+2d)}{a+d}$

19. amistre64

$2 \ =^? \frac{-a -(a+2d)}{a+d}$ $2 \ =^? \frac{-a -a-2d}{a+d}$ $2 \ =^? \frac{-2a-2d}{a+d}$ $2 \ =^? -2\frac{a+d}{a+d};F$

20. amistre64

-1,-2 would then seem to be appropriate to me

21. anonymous

Is it? I wrote (-1, -2), just guessing.

22. asnaseer

amistre: I get a different result. Aadarsh: what do you get?

23. amistre64

i got a typo in my cerbral cortex; :) 1,-2 might be better; would have to test it out

24. asnaseer

:) - I concur

25. anonymous

Yes, (1, -2) is the only correct answer.